A study of {\textrm{v}}-number for some monomial ideals
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Biswas, Prativa
[1]
;
Mandal, Mousumi
[1]
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[1] Indian Institute of Technology Kharagpur
Indian Institute of Technology Kharagpur
India
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- Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 76, Fasc. 3, 2025, págs. 667-682
- Idioma: inglés
- DOI: 10.1007/s13348-024-00451-x
- Texto completo no disponible (Saber más ...)
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Resumen
In this paper, we give formulas for {\textrm{v}}-number of edge ideals of some graphs like path, cycle, 1-clique sum of a path and a cycle, 1-clique sum of two cycles and join of two graphs. For an {\mathfrak {m}}-primary monomial ideal I\subset S=K[x_1,\ldots ,x_t], we provide an explicit expression of {\textrm{v}}-number of I, denoted by {\textrm{v}}(I), and give an upper bound of {\textrm{v}}(I) in terms of the degree of its generators. We show that for a monomial ideal I, {\textrm{v}}(I^{n+1}) is bounded above by a linear polynomial for large n and for certain classes of monomial ideals, the upper bound is achieved for all n\ge 1. For {\mathfrak {m}}-primary monomial ideal I we prove that {\textrm{v}}(I)\le {\text {reg}}(S/I) and their difference can be arbitrarily large.
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